Prediction of microdrill breakage using rough sets

Abstract

This study attempts to correlate the nonlinear invariants’ with the changing conditions of a drilling process through a series of condition monitoring experiments on small diameter (1 mm) drill bits. Run-to-failure tests are performed on these drill bits, and vibration data are consecutively gathered at equal time intervals. Nonlinear invariants, such as the Kolmogorov entropy and correlation dimension, and statistical parameters are calculated based on the corresponding conditions of the drill bits. By intervariations of these values between two successive measurements, a drop–rise table is created. Any variation that is within a certain threshold (+-20% of the measurements in this case) is assumed to be constant. Any fluctuation above or below is assumed to be either a rise or a drop. The reduct and conflict tables then help eliminate incongruous and redundant data by the use of rough sets (RSs). Inconsistent data, which by definition is the boundary re-gion, are classified through certainty and coverage factors. By handling inconsistencies and redundancies, 11 rules are ex-tracted from 39 experiments, representing the underlying rules. Then 22 new experiments are used to check the validity of the rule space. The RS decision frame performs best at predicting no failure cases. It is believed that RSs are superior in dealing with real-life data over fuzzy set logic in that actual measured data are never as consistent as here and may dominate the monitoring of the manufacturing processes as it becomes more widespread.